Thursday, January 6, 2011

Three Part Lesson: Mean

This is the three-part problem solving math lesson we observed in Justus' Grade 5/6 class during our visit.

Background of the Students/Class
Prior to this lesson, students had experience determining the mode, median, and mean of a set of numbers.  This lesson was a consolidation of the Data Management unit and served as a review before the unit test.

Justus uses the three-part lesson format regularly and aims to use the math congress consolidation strategy at least once a week.  In his words, 'the kids cheer when it's a congress day!".

The Lesson
Part 1: Activation of prior knowledge/schema
Justus wrote a group of numbers on the blackboard.  Students were asked to calculate the mean and the median of the set.  Students were given the choice to use a calculator to do this.

The goal of this part of the lesson was to ensure that students were able to calculate the mean of a set of data accurately.  Since the class was able to do this, Justus moved on to the problem.

Part 2: Working on It
Each student was given a copy of the problem to read on their own or possibly start solving it.
Grade 6 EQAO: Spring 2010 (#9)
Justus ensured that everyone understood the problem by completing a KWC chart with the class.  

Students worked in pairs to solve the problem.  Justus shared with us that since most of his students were around the same level, he allows them to choose their partner.  He finds that this strategy works for his class because his students are always on task and produce quality work.

During this time, Justus circulated and chose specific pairs to share their thinking with the whole class during the math congress.

Part 3: Reflecting and Connecting (Consolidation)
Prior to the math congress, Justus prefers to put all  of the student thinking on display.  This is a strategy he uses to manage the combined grade.  Students are exposed to the difference in the complexity/level/detail of each grade level's work. 

Once this was done, pairs were asked to share their thinking with the whole class.  Justus prefers that one member of a pair/triad present to invite active participation by all.  Here are three solutions that were shared with the whole class.

Sample #1: This solution was shared because of the error (misconception).  Two pairs shared the same thinking so Justus wanted it addressed during the congress.
Sample #2: This pair was asked to share their thinking because it was unique to the class (no one else thought of it like this, including all the teachers in the room!)

After this sharing was done, the rest of the class was invited to ask questions, make comments/connections etc.

Justus uses the consolidation portion of the lesson to give students/whole class feedback about their solution and/or thinking.  
The feedback he gave the class included specific comments about:
- organization of calculations
- crossing out work/thinking  
- justification (some groups did not do it)

Explicit Teaching
Since every pair was able to solve the problem in an effective way, Justus did not have to explicitly teach the concept of mean.  Rather, he focused on clarifying a particular misconception in student work, such as Sample #1.

By the end of the lesson, Justus concluded that his students understood the concept of mean and were ready for their unit test.

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